Related papers: Quantum stochastic differential equations and cont…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…
The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of…
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
The stochastic Schr\"odinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties…
This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the…
"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open…
Universal quantum computation encoded over continuous variables can be achieved via Gaussian measurements acting on entangled non-Gaussian states. However, due to the weakness of available nonlinearities, generally these states can only be…
Hardy's theorem states that the hidden variables of any realistic theory of quantum measurement, whose predictions agree with ordinary quantum theory, must have a preferred Lorentz frame. This presents the conflict between special…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…
We derive the quantum stochastic master equation for bosonic systems without measurement theory but control theory. It is shown that the quantum effect of the measurement can be represented as the correlation between dynamical and…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…